Gauge invariance in fractional field theories

R. Herrmann
The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order $o(\bar{g})$ in the coupling constant $\bar{g}$. As a first application, based on the Riemann-Liouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately.
The transformation properties of the non relativistic fractional Schrödinger-equation under spatial rotations are investigated and an internal fractional spin is deduced.

download: arxiv:0708.2262v2 [math-ph]
reference: doi:Physics Letters A 372 (2008) 5515-5522